The Roman Empire grew to be huge. It covered most of Europe, North Africa, and parts of Asia. Just getting messages from Rome to the outer parts of the Empire took weeks. The Empire had become too large to rule effectively. The outer provinces were pretty much doing whatever they wanted.
Emperor Diocletian was looking for a way to fix this and other problems. He decided that the only thing to do was to actually break the empire into two pieces. One piece would be the western empire, based in Rome. The other would be the eastern empire, based in Byzantium. There would be two emperors, one in charge of each piece, working together against outside enemies, but each ruling their half separately.
This turned out to be a very good plan at least for the Eastern half of the empire. When the Western Roman empire collapsed, the Eastern Empire continued for another thousand years.